Horizontal Sigma Coordinate System for River-Flow Models

Abstract

Because of complicated channel geometry, horizontal coordinates are important in accurate and efficient computations of river flow. We propose a simplified horizontal coordinate system for river-flow simulation, referred to here as a horizontal sigma coordinate system that uses boundary-fitted grids along river channels like a generalized curvilinear coordinate system, without losing the simplicity of Cartesian or orthogonal curvilinear coordinate systems. The proposed approach is based on a sigma coordinate system. The depth-averaged continuity and momentum equations for horizontal two-dimensional fluid motion in the Cartesian and orthogonal curvilinear coordinate systems are transformed to those in the horizontal sigma coordinate system. The form of the transformed continuity and momentum equations in the proposed system is a fairly minor modification of the form of the equations for the Cartesian and orthogonal curvilinear coordinate systems. Computational results for a straight open-channel flow with a narrow pass indicate that the horizontal sigma coordinate system is as numerically accurate as the generalized curvilinear coordinate system and that the CPU times required to calculate the horizontal sigma and Cartesian coordinate systems are comparable. We also computed flood flow in an actual river using the numerical models based on the horizontal sigma, orthogonal curvilinear, and generalized curvilinear coordinate systems. The results show that the horizontal sigma coordinate system may dramatically reduce the numerical error generated in the orthogonal curvilinear coordinate system. These facts demonstrate that the horizontal sigma coordinate system is a promising tool for numerical approximation of flow in the horizontal direction that is computationally efficient and numerically accurate.